Area and Volume Flashcards

A sector has area 20π and radius 10. What is the central angle of the sector?

Answer: 72°

Sector area = (θ/360°)πr² → 20π = (θ/360°)(100π) → θ/360° = 1/5 → θ = 72°.

A rectangular sheet of paper 24 cm × 18 cm is rolled into an open cylinder along its 24 cm edge. What is the volume of the cylinder? (Use π ≈ 3.14)

Answer: 823.68 cm³

Circumference = 24 → r = 24/(2π) = 24/6.28 ≈ 3.82 cm; V = π(3.82²)(18) ≈ π(14.59)(18) ≈ 823.68 cm³.

The area of a right triangle is 40 cm² and one leg is 10 cm. What is the hypotenuse?

Answer: √164 cm

Area = (1/2)(10)(h) = 40 → h = 8 cm; hypotenuse = √(10² + 8²) = √(100 + 64) = √164 cm.

A building has a base that is an isosceles trapezoid with parallel sides 20 m and 30 m and height 8 m. How much floor space (area) does it cover?

Answer: 200 m²

A = ½(b₁ + b₂)h = ½(50)(8) = 200 m².

A cuboid has dimensions 3 × 4 × 5. It is cut in half by a plane parallel to the 4 × 5 face. What is the surface area of one resulting piece?

Answer: 74

Each half has dimensions 1.5 × 4 × 5; SA = 2(1.5×4 + 1.5×5 + 4×5) = 2(6 + 7.5 + 20) = 67.

A semicircle has diameter 20 cm. What is the perimeter of the semicircle? (Use π ≈ 3.14)

Answer: 51.4 cm

Perimeter = πr + 2r = π(10) + 20 = 31.4 + 20 = 51.4 cm.

A box without a lid has dimensions 8 × 5 × 3. What is the total surface area of the box (no top)?

Answer: 118

Bottom = 8×5 = 40; two long sides = 2(8×3) = 48; two short sides = 2(5×3) = 30; total = 118.